Question: Simplify the following expression: $ k = \dfrac{-4q}{4q - 1} + \dfrac{9}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-4q}{4q - 1} \times \dfrac{7}{7} = \dfrac{-28q}{28q - 7} $ Multiply the second expression by $\dfrac{4q - 1}{4q - 1}$ $ \dfrac{9}{7} \times \dfrac{4q - 1}{4q - 1} = \dfrac{36q - 9}{28q - 7} $ Therefore $ k = \dfrac{-28q}{28q - 7} + \dfrac{36q - 9}{28q - 7} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-28q + 36q - 9}{28q - 7} $ $k = \dfrac{8q - 9}{28q - 7}$